text:
\section{Introduction}
In the last decades, automatic analysis of human motion has been an active research topic, with applications that have been exploited in a number of different contexts, including video surveillance, semantic annotation of videos, entertainment, human computer interaction and home care rehabilitation, to say a few.
Differences in body proportion (size, height, corpulence), body stiffness and training, influence the way different people perform an action. Even one same person is not able to perform the same action twice, exactly replicating the same sequence of body poses in space and time. This variability makes the task of human motion analysis very challenging.

For years, the approaches could be distinguished in two main classes: those operating on pixel values extracted from the RGB stream (either stacking groups of consecutive frames or extracting motion vectors) and those building upon the higher level representation of body skeletons.
These latter approaches were supported by the diffusion of low-cost RGB-D cameras (such as the Microsoft Kinect) that can operate in real-time, while reliably extracting the 3D coordinates of body joints.
More recently, deep CNN architectures have demonstrated real-time and accurate extraction of the coordinates of body joints from RGB streams~\cite{cao2017realtime}.
These advances make it possible to use a skeleton-based body representation in a much broader range of domains and operative contexts than before, being not limited by the short operative range of RGB-D sensors that typically operate indoor and in the range of a few meters.
The design of the recognition/classification module on top of the body skeleton representation makes it possible to describe an action as a sequence of body poses, each one corresponding to a point in a feature space, whose dimension is proportional to the number of body joints.
By exploiting the geometric properties of the manifold where these pose descriptors lie, it is possible to define a similarity metric that is invariant under translation, scaling, rotation and also under variations of the speed of execution of the action.
Furthermore, the explicit representation of an action as a trajectory, \emph{i.e.}, a sequence of poses, on the manifold makes it possible to extract statistical summaries, such as mean and deviation from the mean, from a group of actions.
Through these summaries, one action can be better characterized for the purpose of detecting outliers corresponding to the anomalous execution of an action, that can be of particular relevance for action prediction.
In fact, when analyzing the skeleton sequences, there are four main aspects to challenge: (1) A shape representation invariant to undesirable transformations; (2) A temporal modeling of landmark sequences; (3) A suitable rate-invariant distance between arbitrary sequences, and (4) A solution for temporal sequence classification.

This paper lies in the continuity of recent works that model the comparison and classification of temporal sequences of landmarks on the Riemannian manifold of positive-semidefinite matrices. Building on the work~\cite{KacemPAMI2019}, our approach involves four different steps: 1) We build a trajectory on the Riemannian manifold from the body skeletons; 2) We apply a curve fitting algorithm on the trajectories to denoise the data points; 3) We perform a temporal alignment using a Global Alignment Kernel, defining a positive-semidefinite kernel; 4) Finally, we use this kernel with a classic SVM to classify the actions. An overview of the full approach is given in Fig.~\ref{Fig:AppOverview}.

\begin{figure*}[!ht]
  \centering
    \includegraphics[width=0.85\textwidth]{Overview-ICCV.png}
    \caption{Overview of the proposed approach - After automatic body skeletons detection for each frame of a sequence, the Gram matrices are computed to build the trajectory on the $\mathcal{S}^+(d,n)$ manifold. We apply a curve fitting algorithm on the trajectory to smooth the curve and reduce noise. Global Alignment Kernel (GAK) is then used to align the trajectories on the manifold. Finally, we use the kernel generated from GAK with SVM to classify the actions.}
    \label{Fig:AppOverview}
\end{figure*}

The novelties with respect to~\cite{KacemPAMI2019} are:
\begin{itemize}
\item The manifold of positive-semidefinite matrices is here endowed with a different metric;
\item A recent curve fitting method is used to smooth trajectories on the manifold;
\item We use Global Alignment Kernel for temporal alignment, instead of Dynamic Time Warping.
\end{itemize}

The rest of the paper is organized as follows: in Section~\ref{sect:2}, we summarize the closest works in the literature. In Section~\ref{sect:3}, we explain how we represent our data on the manifold of fixed-rank positive-semidefinite matrices, and present the Riemannian metric that we will use in this paper. In Section~\ref{sect:4}, we describe the curve fitting algorithm that we will use to denoise the trajectories. The curve alignment method and the classifier are presented in Section~\ref{sect5:classification}, while results and discussions are reported in Section~\ref{sect:exp-results}. Finally, in Section~\ref{sect:conclusion}, we conclude and draw some perspectives of the work.

\section{Related Work}\label{sect:2}
A detailed review of the many approaches to human action recognition and classification is out of the scope of this paper. The interested reader can refer to~\cite{kong-2018} for a detailed and updated survey.
In the following, we focus on approaches that use body skeletons as inputs to the recognition/classification module.

One of the first approaches to perform action recognition by the analysis of trajectories of tracked body interest points was presented in Matikainen \etal~\cite{Matikainen_2009_6466}.
Despite the promising results obtained, the authors did not take into account the geometric information of the trajectories.
More recently, in the case of human skeleton in RGB-D images, Devanne \etal~\cite{Devanne2015Cybernetics}
proposed to formulate the action recognition task as the problem of computing a distance between trajectories generated by the joints moving during the action. An action is then interpreted as a normalized parameterized curve in $\mathbb{R}^N$. However, this approach does not take into account the relationship between the joints.
In the same direction, Su \etal~\cite{Su2014} proposed a metric that considers time-warping on a Riemannian manifold, thus allowing the registration of trajectories and the computation of statistics on the trajectories. Su \etal~\cite{Su_2014_CVPR} applied this framework to the problem of visual speech recognition. Similar ideas have been developed by Ben Amor \etal{}~\cite{amor2016action} on the Kendall's shape space with application to action recognition using rate-invariant analysis of skeletal shape trajectories.

Anirudh \etal~\cite{AnirudhTSS17} started from the framework of Transported Square-Root Velocity Fields (TSRVF), which has desirable properties including a rate-invariant metric and vector space representation. Based on this framework, they proposed to learn an embedding such that each action trajectory is mapped to a single point in a low-dimensional Euclidean space, and the trajectories that differ only in the temporal rate map to the same point. The TSRVF representation and accompanying statistical summaries of Riemannian trajectories are used to extend existing coding methods such as PCA, KSVD, and Label Consistent KSVD to Riemannian trajectories. In the experiments, it is demonstrated that such coding efficiently captures distinguishing features of the trajectories, enabling action recognition, stroke rehabilitation, visual speech recognition, clustering, and diverse sequence sampling.

In~\cite{vemulapalli2014human}, Vemulapalli \etal proposed a Lie group trajectory representation of the skeletal data on a product space of special Euclidean ($SE$) groups. For each frame, this representation is obtained by computing the Euclidean transformation matrices encoding rotations and translations between different joint pairs. The temporal evolution of these matrices is seen as a trajectory on $SE(3) \times \cdots \times SE(3)$ and mapped to the tangent space of a reference point. A one-versus-all SVM, combined with Dynamic Time Warping and Fourier Temporal Pyramid (FTP) is used for classification. One limitation of this method is that mapping trajectories to a common tangent space using the logarithm map could result in significant approximation errors. Aware of this limitation, in~\cite{vemulapalli2016rolling} the same authors proposed a mapping combining the usual logarithm map with a rolling map that guarantees a better flattening of trajectories on Lie groups.

More recently, Kacem \etal~\cite{KacemPAMI2019} proposed a geometric approach for modeling and classifying dynamic 2D and 3D landmark sequences based on Gramian matrices derived from the static landmarks. This results in an affine-invariant representation of the data. Since Gramian matrices are positive-semidefinite, the authors relies on the geometry of the manifold of fixed-rank positive-semidefinite matrices, and more specifically, to the metric investigated in~\cite{Bonnabel2009SIAM}. However, this metric is parametrized, and the parameter should ideally be learned from the data. In addition, this paper adopts Dynamic Time Warping for sequence alignment. The resulting distance does not generally lead to a positive-definite kernel for classification.

All the approaches described above rely on the use of \textit{hand-crafted features} enabling representation of the action as a trajectory or point in some suitable manifold. Differently from these approaches, many neural network models have been proposed that rely on training for the extraction of \textit{deep learned features}.
Recurrent neural networks (RNNs) and particularly Long-Short-Term Memory Networks (LSTMs) have been used to perform action recognition by the analysis of sequences of skeleton poses~\cite{Zhu-2016}. However, these methods typically lose structural information when converting the skeleton data and joint connectivity into the vector-shaped input of the neural network. As an alternative, some approaches introduce Convolutional Neural Networks (CNNs)~\cite{Chao-2017} and Graph Convolutional Networks (GCNs)~\cite{Yan-2018,Li-2019} in the overall architecture so as to retain the structural information among joints of the skeleton.
Although these approaches result in state-of-the-art performance~\cite{Gao-2019} on public action recognition benchmarks, it is not possible to define a formal mathematical framework to compute a valid metric on the internal, learned feature representation so as to perform a statistical analysis of the learned actions.

\section{Our Approach}\label{sect:3}
\subsection{Shape Representation}
To represent body movement dynamics, we rely on the time series made of the coordinates of the $n$ tracked body points (\emph{i.e.}, $p_1 = (x_1,y_1), \ldots, p_{n} = (x_{n},y_{n})$ in 2D, or $p_1 = (x_1,y_1,z_1), \ldots, p_{n} = (x_{n},y_{n},z_n)$ in 3D), during each video sequence.
Each video sequence is thus characterized by a set of landmark configurations $\{Z_0,\ldots, Z_{\tau}\}$, where $\tau$ is the number of frames of the video sequence, and where each configuration matrix $Z_{i}$ $(1 \leq i\leq \tau) \in  \mathrm{R}^{n \times d}$ encodes the position of the $n$ landmarks in $d$ dimensions (with $d = 2$ or $d = 3$). We aim to measure the dynamic changes of the curves made of the landmark configurations, remaining invariant to rotation and translation.
Similarly as in~\cite{KacemPAMI2019}, this goal is achieved through a Gram matrix representation, where we compute the Gram matrices as:
\begin{equation}
\label{eq:gram}
G=Z Z^T\; .
\end{equation}

These Gram matrices are $n \times n$ positive-semidefinite matrices, of rank smaller than or equal to $d$ (always equal to $d$ in the datasets considered). Conveniently for us, the Riemannian geometry of the space ${\mathcal S}^+(d,n)$ of $n \times n$ positive-semidefinite matrices of rank $d$ has been studied in~\cite{Bonnabel2009SIAM,journee2010low,vandereycken2009embedded,vandereycken2013riemannian,Massart2018, massart2019curvature}, and used in, \emph{e.g.},~\cite{faraki2016image,meyer2011regression,gousenbourger2017piecewise, massart2019interpolation}.

A classical approach in the design of algorithms on manifolds consists in resorting to first order local approximations on the manifold, called tangent spaces. This requires two tools: the Riemannian exponential (that allows us to map tangent vectors from the tangent space to the manifold), and the Riemannian logarithm (mapping points from the manifold to the tangent space).

In~\cite{KacemPAMI2019}, the manifold $\psd{d}{n}$ is identified to the quotient manifold $(\mathrm{St}(d,n) \times \mathcal{P}_d)/\mathcal{O}_d$, where $\mathrm{St}(d,n) := \{  Y \in \mathbb{R}^{n \times d} \rvert Y^T Y = I_d \}$ is the Stiefel manifold, $\mathcal{P}_d$ is the manifold of $d \times d$ positive-definite matrices, and $\mathcal{O}_d$ is the orthogonal group in dimension $d$. We consider here another representation of the manifold $\psd{d}{n}$, that will result in different expressions for the distance between two points, the Riemannian exponential and logarithm.

\subsection{The Quotient Manifold $\frmat{n}{d} / \mathcal{O}_d$}\label{metrics}

We consider here the identification of $\psd{d}{n}$ to the quotient manifold $\frmat{n}{d} / \mathcal{O}_d$, where $\frmat{n}{d}$ is the set of full-rank $n \times d$ matrices. This geometry has been studied in~\cite{journee2010low,Massart2018,massart2019curvature}.

The identification of $\psd{d}{n}$ with the quotient $\frmat{n}{d} / \mathcal{O}_d$ comes from the following observation. Any PSD matrix $G \in \psd{d}{n}$ can be factorized as $G = ZZ^T$, with $Z \in \frmat{n}{d}$. However, this factorization is not unique, as any matrix $\tilde Z := ZQ$, with $Q \in \mathcal{O}_d$, satisfies $\tilde Z \tilde Z^T = Z QQ^T Z^T = G$. The two points $Z$ and $\tilde Z$ are thus \emph{equivalent} with respect to this factorization, and the set of equivalent points
\[
Z \mathcal{O}_d := \{  ZQ | Q \in \mathcal{O}_d \},
\]

\noindent
is called the equivalence class associated to $G$. The quotient manifold $\frmat{n}{d} / \mathcal{O}_d$ is defined as the set of equivalence classes. The mapping $\pi : \frmat{n}{d} \to \frmat{n}{d} / \mathcal{O}_d$, mapping points to their equivalence class, induces a Riemannian metric on the quotient manifold from the Euclidean metric in $\frmat{n}{d}$. This metric results in the following distance between PSD matrices:
\begin{equation}
\label{eq:PSD-norm}
    d(G_i, G_j) = \left[  \mathrm{tr}(G_i) + \mathrm{tr}(G_j) - 2 \mathrm{tr}\left( \left( G_i^{\frac{1}{2}}  G_j G_i^{\frac{1}{2}} \right)^{\frac{1}{2}} \right) \right]^{\frac{1}{2}}.
\end{equation}

This distance can be expressed in terms of the landmark variables $Z_i, Z_j \in \frmat{n}{d}$ as follows:
\begin{equation}
\label{eq:frob-norm-new-metrix}
d(G_i, G_j) = \min_{Q \in \mathcal{O}_d} \lVert Z_jQ-Z_i\rVert_F.
\end{equation}

\noindent
The optimal solution is $Q^* := VU^\top \!$, where $Z_i^\top \! Z_j = U \Sigma V^\top \!$ is a singular value decomposition.

As stated by the next theorem, when $d = 2$, the distance can also be formulated as follows:

\begin{theorem}
\label{theo1}
Let $G_i, G_j \in \psd{2}{n}$ be two Gram matrices, obtained from landmark matrices $Z_i, Z_j \in \mathbb{R}^{n \times 2}$. The Riemannian distance~\eqref{eq:PSD-norm} can be expressed as:
\begin{equation}
\label{eq:distp2}
\resizebox{1\hsize}{!}{$d(G_i, G_j)= \left( \Tr(G_i) - 2\sqrt{(a + d)^2 + (c - b)^2} + \Tr(G_j) \right)^{\frac{1}{2}}$},
\end{equation}
\end{theorem}

\noindent
where $Z_j^TZ_i$ = $\left( \begin{array}{cc} a & b \\ c & d \end{array} \right)$.
\begin{proof}
See Appendix.
\end{proof}

Expressions for the Riemannian exponential and logarithm are given in~\cite{Massart2018}. We used the implementations provided in the Manopt toolbox~\cite{manopt}.

\section{Trajectory Modeling}\label{sect:4}
The dynamic changes of body joints movement are characterized by trajectories on the Riemannian manifold of positive-semidefinite matrices of fixed rank (see Fig.~\ref{Fig:AppOverview}). More specifically, we fit a curve $\beta_G$ to a sequence  of landmark configurations $\{Z_0, \ldots, Z_\tau\}$ represented by their corresponding Gram matrices $\{G_0,\ldots,G_\tau\}$ in $\mathcal{S}^+(d,n)$. This curve will enable us to model the spatio-temporal evolution of the elements on $\mathcal{S}^+(d,n)$.

Modeling a sequence of landmarks as a piecewise-geodesic curve on $\mathcal{S}^+(d,n)$ showed very promising results when the data are well acquired, \emph{i.e.}, without tracking errors or missing data, see~\cite{KacemPAMI2019, KacemICCV17, OtberdoutBMVC2018}. To account for both missing data and tracking errors, we rely on a more recent curve fitting algorithm: fitting by composite cubic blended curves, proposed in~\cite[\S 5]{Gousenbourger2018}. Specifically, given a set of points $G_0,\ldots,G_\tau \in \mathcal{S}^+(d,n)$ associated to times $t_0, \dots, t_\tau$, with $t_i := i$, the curve $\beta_G$, defined on the interval $[0,\tau]$, is defined as:
\[
\beta_G(t) := \gamma_i(t-i), \qquad t \in [i, i+1],
\]

\noindent
where each curve $\gamma_i$ is obtained by blending together fitting cubic B\'ezier curves computed on the tangent spaces based on the data points $d_i$ and $d_{i+1}$.

These fitting cubic B\'ezier curves depend on a parameter $\lambda$, allowing us to balance two objectives: proximity to the data points at the associated time instants, and regularity of the curve (measured in terms of mean square acceleration). A high value of $\lambda$ results in a curve with possibly high acceleration, but that will almost interpolate the data, while taking $\lambda \rightarrow 0$ will result in a geodesic. The interested reader can refer to~\cite[\S 5]{Gousenbourger2018} for more information about the curve fitting procedure.

\section{Classification}\label{sect5:classification}
Now that we have defined how to represent a sequence and how to compare two distinctive landmark configurations, we present in this section how we compare two landmark sequences and how to classify the actions performed in these same sequences.

\subsection{Global Alignment}\label{global-alignment-kernel}
As we described in Section~\ref{sect:4}, we represent a sequence as a trajectory of Gram matrices in $\psd{d}{n}$. The sequences represented in this manifold can be of different length as the execution rate of the actions can vary from one person to another, meaning that we can not effectively compare them. A common method to do so is to use Dynamic Time Warping (DTW) as proposed in several works~\cite{amor2016action, KacemPAMI2019, gritai2009matching}. However, DTW does not define a proper metric and can not be used to derive a valid positive-definite kernel for the classification phase. To address the problem of non positive definiteness of the kernel defined by DTW, Cuturi \etal~\cite{CuturiVBM07} proposed the Global Alignment Kernel (GAK), which allows us to derive a valid positive-definite kernel when aligning two time series. More recently Otberdout \etal~\cite{Otberdout2019} have proposed to classifiy deep trajectories in SPD manifold using GAK. The generated kernel can be used directly with Support Vector Machine (SVM) for the classification phase, whereas it is not the case with kernels generated with DTW. In fact, the kernels built with DTW do not show favorable positive definiteness properties as they rely on the computation of an optimum rather than the construction of a feature map. Note that the computation of the kernels with GAK can be done in quadratic complexity, similarly to naive implementation of DTW. The next paragraph describes how to compute the similarity score between two sequences, using this Global Alignment Kernel.

Let us now consider $Z^1= \{Z^1_0,\cdots, Z^1_{\tau_1}\}$ and $Z^2=\{Z^2_0,\cdots, Z^2_{\tau_2}\}$, two sequences of landmark configuration matrices. Given a metric to compute the distance between two elements of each sequence, we propose to compute the matrix $D$ of size $\tau_1 \times \tau_2$, where each $D(i,j)$ is the distance between two elements of the sequences, with $1 \leq i \leq \tau_1$ and $1 \leq j \leq \tau_2$.
\begin{equation}
\label{eq:matrix-distance}
    D(i,j) = d(Z^1_i, Z^2_j) .
\end{equation}

The kernel $\tilde{k}$ can now be computed using the halved Gaussian Kernel on this same matrix $D$. Therefore, the kernel $\tilde{k}$ can be defined as:
\begin{equation}
\label{eq:k-tilde}
    \tilde{k}(i,j) = \frac{1}{2} * exp\left(-\frac{D(i,j)}{\sigma^2}\right).
\end{equation}
 As reported in~\cite{CuturiVBM07}, we can redefine our kernel such as:
\begin{equation}
\label{eq:kernel-PSD}
    k(i,j) = \frac{\tilde{k}(i,j)}{(1-\tilde{k}(i,j))} .
\end{equation}
This strategy assures us that the kernel is positive semi-definite and can be used in its own. Finally, we can compute the similarity score between the two sequences $Z^1$ and $Z^2$. Remember that this computation is performed in quadratic complexity, like DTW. To do so, we define a new matrix $M$ that will contain the path to the similarity between our two sequences. We define $M$ as a zeros matrix of size $(\tau_1+1) \times (\tau_2+1)$ and $M_{0,0} = 1$. Computing the terms of $M$ is done using Theorem 2 in~\cite[\S 2.3]{CuturiVBM07}:
\begin{equation}
\label{eq:matrix-similarity}
    M_{i,j} = (M_{i,j-1} + M_{i-1,j-1} + M_{i-1,j})*k(i,j) .
\end{equation}

The similarity score we seek is the value at $M_{(\tau_1+1),(\tau_2+1)}$. Algorithm~\ref{algo:similarity} describes all the steps to get the similarity score.

Finally, we build a new matrix $K$ of size $n_{seq} \times n_{seq}$, where $n_{seq}$ is the number of sequences in the dataset we test. This matrix is symmetric and contains all the similarity scores between all the sequences of the dataset and it is used as the kernel for the classification phase with SVM. As this matrix is built with values computed from positive semi-definite kernel, it is a positive semi-definite matrix itself.

\begin{algorithm}
\caption{Computing the similarity score between two sequences using Global Alignment Kernel~\cite{CuturiVBM07}
\label{algo:similarity}}
\DontPrintSemicolon
\SetKwInOut{Input}{input}\SetKwInOut{Output}{output}
\Input{Two sequences of landmark configurations $Z^1= \{Z^1_0,\cdots, Z^1_{\tau_1}\}$, where $Z^1_{0 \leq i \leq \tau_1}$ and $Z^2=\{Z^2_0,\cdots, Z^2_{\tau_2}\}$, where $Z^2_{0 \leq j \leq \tau_2}$.}
\Output{The similarity score between two sequences $Z^1, Z^2$}
$\tilde{k} \longleftarrow \frac{1}{2}*exp\left(-\frac{D(Z^1, Z^2)}{\sigma^2} \right)$ Equations ~\eqref{eq:matrix-distance} and \eqref{eq:k-tilde} \\

\For{$i \leftarrow 0$ \KwTo $\tau_1$}{
    \For{$j \leftarrow 0$ \KwTo $\tau_2$}{
        $k(i,j) \longleftarrow \frac{\tilde{k}(i,j)}{(1 - \tilde{k}(i,j))}$ Equation~\eqref{eq:kernel-PSD}
    }
}

$M \longleftarrow zeros(\tau_1+1, \tau_2+1)$ \\
$M_{0,0} \longleftarrow 1$ \\

\For{$i \leftarrow 1$ \KwTo $\tau_1+1$}{
    \For{$j \leftarrow 1$ \KwTo $\tau_2+1$}{
        $M_{i,j} \longleftarrow (M_{i,j-1} + M_{i-1,j-1} + M_{i-1,j})*k(i,j)$ See Equation~\eqref{eq:matrix-similarity}
    }
}
$similarity \longleftarrow M_{\tau_1+1, \tau_2+1}$

\Return similarity, the similarity score between $Z^1$ and $Z^2$
\end{algorithm}

\subsection{Classification with SVM}
Our trajectory representation reduces the problem of landmark sequence classification to that of trajectory classification in $\mathcal{S}^+(d,n)$. Given that GAK provides a valid PSD kernel as demonstrated by Cuturi \etal{}~\cite{CuturiVBM07}, and given that our local kernel $K$ satisfies this condition as discussed before, we use the standard SVM with the $K$ kernel that represents the matrix containing the similarity scores between all the sequences of a dataset to classify the aligned trajectories with global alignment on $\mathcal{S}^+(d,n)$.

By contrast, DTW may define a non positive definite kernel. Hence, we adopt the pairwise proximity function SVM (ppfSVM), which assumes that instead of a valid kernel function, all that is available is a proximity function without any restriction.
That is, let us consider $\mathcal{T} = \{\beta_G~:[0,1]\rightarrow \mathcal{S}^+(d,n)\}$, the set of time-parameterized trajectories of the underlying manifold. Like in~\cite[\S 4.1]{KacemPAMI2019}, we define a matrix $D_{dtw}$ containing the similarity measure between two trajectories aligned with DTW.
In that case, given $m$ trajectories in $\mathcal{T}$, the proximity function $\mathcal{P} : \mathcal{T} \times \mathcal{T} \rightarrow \mathbb{R}^+$ between two trajectories $Z^{1}$ and $Z^{2}$ is defined by,
\begin{equation}
\mathcal{P}(Z^{1}, Z^{2})=D_{dtw}(Z^{1}, Z^{2}) \; .
\end{equation}

\noindent
Using this proximity function, the main idea of ppfSVM is to represent each training example $Z$ with a vector $[\mathcal{P}(Z,Z^1), \dots , \mathcal{P}(Z,Z^m)]^T$. The set of trajectories can be represented by a $m \times m$ matrix $P$, where $P(i,j) = \mathcal{P}(Z^{1}, Z^{2})$, with $1 \leq i,j \leq m$. From this matrix $P$ we can use a classical linear SVM.

\section{Experimental Results}
\label{sect:exp-results}
To validate the proposed approach, we have conducted experiments on three publicly available datasets with 3D and 2D actions: UTKinect-Action3D, KTH-Action and UAV-Gesture. Our experiments followed the experimental settings commonly used for these datasets.

\subsection{UTKinect-Action3D Dataset}
The UTKinect-Action3D dataset~\cite{xia2012view} is a widely used dataset for 3D action recognition. It contains 199 sequences, consisting of 10 actions, namely \textit{walk, sit down, stand up, pick up, carry, throw, push, pull, wave hands} and \textit{clap hands} performed by 10 different subjects. The videos and the skeletons were captured with a Microsoft Kinect and the skeletons are composed of 20 body joints. In our approach, we use the available skeletal joint locations, where each body joint is defined with its $x$, $y$ and $z$ coordinates. Following the same experimental settings of~\cite{TanfousDA18, LiuWDAK18, KeBASB18}, we performed the Leave-One-Out cross validation, meaning that we used one sequence for testing and the rest for training.
Our experimental results are summarized in Table~\ref{results-our-utk}. In particular, the columns are as follows: \emph{Curve Fitting} indicates if we performed the curve fitting algorithm described in Section~\ref{sect:4}; \emph{Lambda} indicates the value of the lambda parameter in curve fitting;
\emph{Alignment Method} indicates if we used the standard DTW to align sequences or GAK as described in Section~\ref{global-alignment-kernel}; \emph{Sigma} indicates the value of the sigma parameter for the Gaussian Kernel when using GAK; and \emph{Results} indicates our scores.

\begin{table}[!ht]
\centering
\caption{Our results on the UTKinect-Action3D dataset}
\begin{adjustbox}{width=0.47\textwidth}
\begin{tabular}{|c|c|c|c|c|}
\hline
\textbf{Curve Fitting} & \textbf{Lambda} & \textbf{Alignment Method} & \textbf{Sigma} & \textbf{Results} \\ \hline
Yes & 0.5 & DTW & - & 97\% \\
No & - & DTW & - & 97.49\% \\ \hline
Yes & 0.5 & GAK & 0.3 & 97.49\% \\
No & - & GAK & 0.3 & \textbf{97.99\%} \\
Yes & 0.5 & GAK & 0.5 & \textbf{97.99\%} \\ \hline
\end{tabular}
\end{adjustbox}
\label{results-our-utk}
\end{table}

The best accuracy that we obtained on this dataset is 97.99\%. Overall, we can say that the application of curve fitting does not increase our results. Our assumption is that the data in this dataset are very clean, and we can loose some information with the application of smoothing on clean data. Note that we obtained better results when using the Global Alignment Kernel rather that DTW.

\begin{table}[H]
\centering
\caption{Comparison of our approach with state-of-the-art results for the UTKinect-Action3D dataset. *: Deep Learning approach}
\begin{adjustbox}{width=0.38\textwidth}
\begin{tabular}{|l|c|c|}
\hline
 & \multicolumn{2}{c|}{\textbf{Protocol}} \\
 \hline
\textbf{Methods} & \textbf{H-H} & \textbf{LOOCV} \\ \hline
Trajectory on ${\mathcal S}^+(d,n)$~\cite{KacemPAMI2019} (2019) & - & 96,48\% \\
SCK+DCK~\cite{KoniuszCP16} (2016) & 98.2\% & - \\
Bi-LSTM~\cite{TanfousDA18} (2018)* & - & 98.49\% \\
LM$^3$TL~\cite{YangDTZLG17} (2017) & - & 98.8\% \\
GCA-LSTM~\cite{LiuWDAK18} (2018)* & - & 99\% \\
MTCNN~\cite{KeBASB18} (2018)* & - & 99\% \\
Hankel \& Gram matrices~\cite{ZhangWGSC16} (2016) & - & \textbf{100\%} \\
\hline
Ours & - & 97.99\% \\
\hline
\end{tabular}
\end{adjustbox}
\label{sota-utk}
\end{table}

In Table~\ref{sota-utk}, we compare our method with recent state-of-the-art results. Overall, our approach achieves competitive results with respect to most recent approaches. We directly compare our results with~\cite{KacemPAMI2019} as we work on the same geometric space of ${\mathcal S}^+(d,n)$ manifold. The main differences between our method and the method in~\cite{KacemPAMI2019} is the use of a different metric and of the Global Alignment Kernel instead of DTW. Our metric is simpler that the metric in~\cite{KacemPAMI2019}, as we do not have to estimate the parameter $k$ used in Eq.~(7) in~\cite{KacemPAMI2019} for distance computation. Furthermore, the $k$ parameter in~\cite{KacemPAMI2019} is more of a constraint as they have to determine its best value for each dataset they test. The use of GAK is also an advantage for us as it defines a positive semi-definite kernel, which is not the case for DTW allowing us to use a classic SVM instead of ppfSVM.

\begin{figure}[H]
    \centering
    \includegraphics[width=0.47\textwidth]{UTK-Comparison-Throw-Push.png}
    \caption{Comparison of two sequences that are confused in UTKinect-Action3D dataset (top: \textit{Throw} action, bottom: \textit{Push} action)}
    \label{qualitative-utk}
\end{figure}

The Figure~\ref{qualitative-utk} presents two sequences that are confused, leading to a misclassification for one of them. In that case, the top action (\emph{i.e.} Throw) is misclassified as the bottom action (\emph{i.e.} Push). One of the reasons can be the position of the arm at the end of the action, which is the same in the two sequences. The \textit{Throw} action is the most confused action in the dataset.

\subsection{KTH-Action Dataset}
The KTH-Action dataset~\cite{kth} is a 2D action recognition dataset. It consists of six actions, namely \textit{boxing, handclapping, handwaving, jogging, running} and \textit{walking} performed by 25 subjects in four different conditions, which are outdoor, outdoor with scale variations, outdoor with different clothes and indoor. The sequences were acquired with a static camera at a frame rate of 25 fps and a resolution of $160 \times 120$ pixels. The dataset contains a total of 599 clips, with 100 clips per actions (1 clip is missing for one action). As the sequences in the dataset are 2D videos, we have to extract the skeletons of the subjects performing the actions. To do so, we used the OpenPose framework~\cite{openpose} to extract the skeletons in the COCO format, with 18 body joints. Note that we clean the landmark sequences by removing the frames where the body joints where not effectively estimated. Keeping all the frames leads to worst results due to misdetected joints, meaning that we do not need all the frames available to recognize an action. Figure~\ref{coco-skeleton} shows the configuration of the body joints that we analyzed. For this dataset, we followed the Leave-One-Actor-Out cross validation protocol, meaning that we use one subject for testing and the rest for training. Table~\ref{results-ours-kth} summarizes our experimental results on this dataset.

\begin{figure}[H]
    \centering
    \includegraphics[width=0.22\textwidth]{coco-body-joints.png}
    \caption{Skeleton with the COCO format.}
    \label{coco-skeleton}
\end{figure}

\begin{table}[H]
\centering
\caption{Our experimental results on the KTH-Action dataset}
\begin{adjustbox}{width=0.47\textwidth}
\begin{tabular}{|c|c|c|c|c|}
\hline
\textbf{Curve Fitting} & \textbf{Lambda} & \textbf{Alignment Method} & \textbf{Sigma} & \textbf{Results} \\ \hline
No & - & DTW & - & 94.49\% \\
Yes & 10 & DTW & - & 94.66\% \\ \hline

No & - & GAK & 0.2 & 95.16\% \\
Yes & 10 & GAK & 0.2 & \textbf{96.16\%} \\ \hline
\end{tabular}
\end{adjustbox}
\label{results-ours-kth}
\end{table}

Here, again, we obtained better results when using the GAK, demonstrating superior performance over DTW. The results reported with DTW are the best accuracy over all the configurations we tested. Unlike the data in UTKinect-Action3D dataset, the data in KTH-Action are 2D and low resolution videos, with presence of noise in the background, leading to noisy skeleton data after extraction. In this regard, the application of the curve fitting algorithm improves our results by 1\%. We compare our approach with the state-of-the-art in Table~\ref{sota-kth}. Overall, our method achieves competitive results with recent approaches, while only using skeletal data.

\begin{table}[H]
\centering
\caption{Comparison of our approach with state-of-the-art results for the KTH-Action dataset. *: Deep Learning approach}
\begin{adjustbox}{width=0.41\textwidth}
\begin{tabular}{|l|c|c|c|}
\hline
\textbf{Methods} & \textbf{Input data} & \textbf{Protocol} & \textbf{Accuracy} \\
\hline
Schüldt \etal~\cite{kth} (2004) & RGB & Split & 71.7\% \\
Liu \etal~\cite{LiuLS09} (2009) & RGB & LOAO & 93.8\% \\
Yoon \etal\cite{YoonK10} (2010) & Skeleton & - & 89\% \\
Raptis \& Soatto~\cite{RaptisS10} (2010) & RGB & LOAO & 94.5\% \\
Wang \etal~\cite{WangKSL11} (2011) & RGB & Split & 94.2\% \\
Gilbert \etal~\cite{GilbertIB11} (2011) & RGB & LOAO & 95.7\% \\
Jiang \etal~\cite{JiangLD12} (2012) & RGB & LOAO & 95.77\% \\
Vrigkas \etal~\cite{VrigkasKNK14} (2014) & RGB & LOAO & \textbf{98.3\%} \\
Veeriah \etal~\cite{VeeriahZQ15} (2015)* & RGB & Split & 93.96\% \\
Liu \etal~\cite{LiuSLL16} (2016) & RGB & Split & 95\% \\
Almeida \etal~\cite{AlmeidaPG17} (2017) & RGB & LOAO & 98\%  \\
\hline
Our & Skeleton & LOAO & 96.16\% \\
\hline
\end{tabular}
\end{adjustbox}
\label{sota-kth}
\end{table}

\subsection{UAV-Gesture Dataset}
The UAV-Gesture dataset~\cite{UAV-Gesture} is a 2D videos dataset, consisting of 13 actions corresponding to UAV (\emph{i.e.}, Unmanned Aerial Vehicles) gesture signals. These actions are \textit{All Clear, Have Command, Hover, Land, Landing Direction, Move Ahead, Move Downward, Move To Left, Move To Right, Move Upward, Not Clear, Slow Down} and \textit{Wave Off}. The actions are performed by 11 different subjects in an outdoor scenario with slight camera movements. The dataset contains 119 high-quality clips consisting of 37151 frames. As reported in~\cite{UAV-Gesture}, this dataset is not primarily designed for action recognition, but it can be used for this specific task. The skeletons are available with the dataset and the OpenPose framework was also used to extract them in the COCO format. Table~\ref{results-ours-uav} compares our results with the baseline experiment reported in~\cite{UAV-Gesture}

\begin{table}[H]
\centering
\caption{Comparison of our approach with the baseline on the UAV-Gesture dataset. *: Deep Learning approach}
\begin{adjustbox}{width=0.478\textwidth}
\begin{tabular}{|c|c|c|c|c|}
\hline
\textbf{Method} & \textbf{Curve Fitting} & \textbf{Lambda} & \textbf{Alignment Method} & \textbf{Results} \\ \hline
P-CNN~\cite{UAV-Gesture} (2018)* & - & - & - & 91.9\% \\ \hline
Ours & No & - & GAK & 91.6\% \\
Ours & Yes & 10 & GAK & \textbf{92.44\%} \\ \hline
\end{tabular}
\end{adjustbox}
\label{results-ours-uav}
\end{table}

This is a very recent dataset and its principal interest does not rely on action recognition, meaning a lack of results to compare our results with. However, the authors have tested their dataset for the case of action recognition based on skeletons with Pose-Based Convolutional Neural Network (P-CNN) descriptors, that gives us a baseline to compare our results.
The baseline achieves an accuracy of 91.9\% with a Deep Learning based approach, whereas our approach achieves an accuracy of 92.44\%, outperforming the state-of-the-art results when applying curve fitting and the GAK alignment method.

The Figure~\ref{qualitative-uav} presents two very similar actions in the dataset, that is \textit{All Clear} and \textit{Not Clear}. The only big difference between these two actions is the orientation of the hand on the raised arm.
This information is not captured when only retrieving the body skeleton from the OpenPose framework, even if it is possible to retrieve the hand skeleton. Note that with our method, the two actions are only confused three time on a total of 22 sequences, meaning that our method is capable of differentiate minimal changes in the actions.

\begin{figure}[H]
    \centering
    \includegraphics[width=0.47\textwidth]{UAV-Comparison-All-Not-Clear.png}
    \caption{Comparison of two sequences that are confused in UAV-Gesture dataset (top: \textit{All Clear} action, bottom: \textit{Not Clear} action)}
    \label{qualitative-uav}
\end{figure}

\subsection{Computation Time Comparison}
In this analysis, we have computed the time for each step of our approach. Applying the curve fitting algorithm can be resource demanding on some manifolds, as it requires successive computations of Riemannian exponentials and logarithms (see~\cite{Gousenbourger2018} for more information on the computational cost of the method). The alignment method can also be resource demanding, regarding the size of the trajectory. With all these parameters in mind, we propose to compute the time that our method takes to compute specific tasks from pose extraction to action classification. The tests were conducted on a laptop equipped with an Intel Core i7-8750H CPU, 16G of RAM and a NVidia Quadro P1000 GPU. Table~\ref{computation-time-kth} and Table~\ref{computation-time-uav} summarize the execution time of each part of our method for the KTH-Action and UAV-Gesture datasets, respectively. For metric notation, $M_1$ refers to Eq.~\eqref{eq:frob-norm-new-metrix} and $M_2$ refers to Eq.~\eqref{eq:distp2}, in Section~\ref{metrics}.

\begin{table}[H]
\centering
\caption{Execution time (in seconds) obtained on the KTH-Action dataset for the different steps of the method for one sequence.}
\begin{adjustbox}{width=0.478\textwidth}
\begin{tabular}{|c|c|c|c|c|}
\hline
\textbf{Pose extraction} & \textbf{Curve Fitting} & \textbf{Alignment method - Metric} & \textbf{Alignment} & \textbf{Classification} \\ \hline
147 & 0.069 & DTW - $M_1$ & 0.034 & 0.41 \\
147 & 0.069 & DTW - $M_2$ & \textbf{0.02} & 0.41 \\ \hline
147 & 0.069 & GAK - $M_1$ & 0.04 & 0.49 \\
147 & 0.069 & GAK - $M_2$ & \textbf{0.019} & 0.49 \\ \hline
\end{tabular}
\end{adjustbox}
\label{computation-time-kth}
\end{table}

\begin{table}[H]
\centering
\caption{Execution time (in seconds) obtained on the UAV-Gesture dataset for the different steps of our method for one sequence.}
\begin{adjustbox}{width=0.478\textwidth}
\begin{tabular}{|c|c|c|c|c|}
\hline
\textbf{Pose extraction} & \textbf{Curve Fitting} & \textbf{Alignment method - Metric} & \textbf{Alignment} & \textbf{Classification} \\ \hline
- & 0.504 & DTW - $M_1$ & 0.128 & 0.038 \\
- & 0.504 & DTW - $M_2$ & \textbf{0.072} & 0.038 \\ \hline
- & 0.504 & GAK - $M_1$ & 0.138 & 0.53 \\
- & 0.504 & GAK - $M_2$ & \textbf{0.066} & 0.053 \\ \hline
\end{tabular}
\end{adjustbox}
\label{computation-time-uav}
\end{table}

For the KTH-Action dataset, we consider a sequence of 61 frames and a sequence of 192 frames for UAV-Gesture. First, we can observe that the pose extraction phase takes most of the execution time for the KTH-Action dataset. This is partially due to the fact that our GPU is not powerful enough (we get around 3.5fps with our Quadro P1000). The extraction time is not reported for the UAV-Gesture dataset as the skeletons are available with the dataset. The second thing we can observe is the low difference in computation time for the alignment part when switching from DTW to GAK. We can also note that when we use $M_2$, the computation time can be reduced by a factor 2 compared to the use of $M_1$, showing that the formula~\eqref{eq:distp2} is in our case cheaper to evaluate than~\eqref{eq:frob-norm-new-metrix}. If we only consider the execution time for the treatment of the skeletons, it takes around 0.499 seconds to classify an action of the KTH-Action dataset and around 0.614 seconds for an action of the UAV-Gesture dataset in the best case scenario.

\section{Conclusion and Future Work}\label{sect:conclusion}
In this paper, we have proposed a method for comparing and classifying temporal sequences of 2D/3D landmarks on the positive semi-definite manifold. Our approach involves three different steps: 1) We build a trajectory on the Riemannian manifold from the body skeletons; 2) we apply a curve fitting algorithm on the trajectories to denoise the data points; 3) we perform a temporal alignment using a Global Alignment Kernel. Our experiments on three publicly available datasets show that the proposed approach gives competitive results with respect to state-of-the-art methods.

\section{Acknowledgements}
We thank Dr. A. Kacem for fruitful discussions. We also thank Prof. J-C. Alvarez Paiva  for fruitful discussions on the formulation of the distance between $n \times 2$ landmarks configurations.

\section{Appendix}
\begin{proof} of Theorem~\ref{theo1}.
We can reformulate our metric introduced in Eq.~\eqref{eq:frob-norm-new-metrix} with:
\begin{align*}
d^2(G_i, G_j) & = \Tr \left[ (Z_jQ - Z_i)(Z_jQ - Z_i)^T \right] \\
  & = \Tr(G_i) - 2\Tr(Z_iQ^TZ_j^T) + \Tr(G_j) .
\end{align*}

To minimize our distance, we need to maximize the term $\Tr(Z_iQ^TZ_j^T)$. Let $Z_j^TZ_i$ be a $2 \times 2$ matrix with four unknown values $a, b, c, d$ and let $Q \in \mathcal{O}_p$, we  maximize:
\begin{equation}
\label{eq:maximize-term}
\begin{split}
    \max\;\Tr \left[ \left( \begin{array}{cc} a\cos{\Theta} - b\sin{\Theta} & - \\ - & c\sin{\Theta} + d\cos{\Theta} \end{array} \right) \right] .
\end{split}
\end{equation}

From Eq.~\eqref{eq:maximize-term} we now have to find the maximum of $(a + d)\cos{\Theta} + (c - b)\sin{\Theta}$, meaning that we have to maximize $\sqrt{(a + d)^2 + (c - b)^2}\cos{(O-O')}$. As we want to maximize this value, $O$ has to be equal to $O'$, so $\sqrt{(a + d)^2 + (c - b)^2}\cos{(O-O')} \leqslant \sqrt{(a + d)^2 + (c - b)^2}$. Therefore we can say that:
\begin{equation}
    \max \Tr(Z_iQ^TZ_j^T) = \sqrt{(a + d)^2 + (c - b)^2} .
\end{equation}
\end{proof}

{\small
\bibliographystyle{ieee}

redpajama_set_name: RedPajamaArXiv


Welcome to Eastside Beer Banter!
Because you are here reading this, I must assume you have an interest in beer and hopefully that interest lies more towards the craft beer end of the beer quality continuum because that is what I will be focusing on here on this blog.
If you are looking for a blog that rates beers, pubs, breweries, etc, you will be mostly disappointed as that is not my purpose. What I hope to write about are issues, trends, ideas and opinions about the craft beer scene, focusing on Vancouver, BC, as that is where I am located. Having said that, my biases about certain beers, pubs and breweries will leak onto these pages and posts because, as a writer, it is impossible to remove one's self from the process to remain completely objective.
I hope you enjoy what you read here and I hope that my words give you food for thought. This blog is more a labour of love than anything else and it allows me to tell my wife that my time spent drinking and talking about craft beer is "research". Please feel free to post feedback and initiate discussion about the ideas posted on this site.
And above all, make sure you have a good craft beer at your side while perusing this blog.
Who ever thought drinking beer could be so political?
How I became a "Beer Geek"
Open Letter to Suzanne Anton & John Yap - Why Is My Happy Hour Beer This Week More Expensive Than My Regularly Priced Beer Last Week?


Home Culture of Awesomeness Awards & Recognition Spread the word about your 2018 sales award!
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Mortgages help us to be able to buy new homes. Down the road you can also purchase a second mortgage. These tips will help you out no matter what type of mortgage you're looking for.
Begin getting ready for a home mortgage well in advance of your application. If you are considering buying a home, you need to prepare your financials asap. It means building a bit of savings and raising your credit score. If you wait too long to do these things, you may not be approved for a home mortgage.
If your house is worth less than what you owe and you've been unsuccessful in refinancing it, try again. HARP is a program that allows homeowners to refinance regardless of how bad their situation may be. Discuss a HARP refinance with your lender. If your lender still refuses to cooperate with you, then find one who will.
Don't go charging up a storm while you are waiting for your mortgage to close. Lenders tend to run another credit check before closing, and they may issue a denial if extra activity is noticed. Hold off on making a big furniture purchase or buying other big ticket items until you have completed the deal.
Most mortgages require you to make a cash down payment. Although zero down payment mortgages were available in the past, most mortgage companies make it a requirement. Find out information on the down payment requirements in advance of submitting any loan application.
Changes in your finances may harm your approval prospects. You should not apply for a mortgage until you have a secure job. You shouldn't get a different job either until you have an approved mortgage because the mortgage provider is going to make a choice based on your application's information.
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Determine what kind of mortgage you are going to need. There are different types of home loans. Understanding these differences will make it simpler to apply it to your own situation, this way you can figure out what works best. Speak to a lender regarding your mortgage options.


Podcast 34 will be a special programme featuring music from Wales, as I will be presenting the podcast from Blaenau Ffestiniog in the heart of Snowdonia National Park. If you are a Welsh poet or musician, or know of any artists who would be interested in having their material on the podcast please contact me at the usual e-mail address.
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text:
Don't Give Up On Ben Roethlisberger Just Yet
Oct. 14, 2017 , at 1:45 PM
By Michael Salfino
Filed under NFL
It's hard to do much worse than Ben Roethlisberger's last game, when he threw five interceptions.
Joe Sargent / Getty Images
The Steelers may be 3-2, but the mood in Pittsburgh is dour. Ben Roethlisberger is coming off a five-interception fiasco against the Jacksonville Jaguars, the latest and worst in a run of lukewarm performances this season. Plenty in Steeler nation are beginning to question whether the 35-year-old Roethlisberger has hit the wall. One of those people is the actual Ben Roethlisberger.
The numbers are definitely not pretty, especially when compared to his career averages. That interception festival he hosted in Week 5 torched his passer rating, which has sunk to 75.8 and is way below his 94.1 career rating entering the season. More alarming than the spate of picks is that Roethlisberger's yards per attempt, which for his career prior to this year stood at a near all-time-best 7.9, is a career-low 6.5 so far this season.
But a closer look at the numbers shows there's good reason to believe that this bad stretch is just that: a bad stretch. Here are the key reasons Steelers fans should still have hope — regardless of what Roethlisberger himself is saying or thinking.
History is on his side
We identified several quarterbacks who struggled in the first five games of their age-35 seasons when compared to what they did through age 34.1 In almost every case, these QBs bounced back to something much closer to their established levels. To be sure, there's some selection bias at play here — most of these quarterbacks are generally excellent, because erratic and unreliable passers do not usually last in the NFL until they are 35.
Struggling 35-year-olds mostly rebounded nicely
Quarterbacks who posted subpar numbers in their first five games during their age-35 season and how they fared in rest of that year, 1978-2017
GAMES 1-5
GAMES 6-16
YPA*
Dan Fouts 1986 SD 81.8 7.8 55.4 6.3 84.0 7.7
Jim Hart 1979 STL 70.6 6.9 49.0 5.7 59.0 6.0
Ben Roethlisberger 2017 PIT 94.1 7.9 75.8 6.5
Jim Kelly 1995 BUF 85.8 7.5 67.8 6.3 87.0 7.1
Trent Green 2005 KAN 87.9 7.7 80.5 6.9 94.3 8.3
Drew Brees 2014 NOR 95.3 7.5 91.8 7.2 99.6 7.7
Brett Favre 2004 GNB 86.9 7.1 86.0 7.1 95.4 7.8
Matt Hasselbeck 2010 SEA 83.3 6.9 74.8 6.4 72.3 7.0
Ken Anderson 1984 CIN 82.0 7.3 68.0 7.7 96.1 7.6
*Through age-34 season.
Minimum 125 passes in first five games, with a QB rating worse than career numbers prior to that season.
Source: Pro-Football-Reference.com
Among the passers on this list, the average QB rating improved from 71.2 in the first five games to 86.0 for the remainder of the season. Their yards per attempt also rebounded, from a pedestrian 6.7 to a solid 7.4, on average. If Roethlisberger improves at the same rate, his passer rating for the rest of the year would be 88.4 and his yards per attempt would bounce up to 7.2. But Hall of Famers Dan Fouts and Jim Kelly beat those averages, so it's certainly possible that Roethlisberger could outperform them as well.
Roethlisberger is still doing Roethlisberger things
While the box scores have been ugly, many of Roethlisberger's underlying numbers have been typical for his career. His accuracy hasn't declined significantly: Only 17.5 percent of his throws have been off target, which is only a shade worse than the 16.9 percent rate he posted in the regular season from 2014 to 2016. And on deep passes,2 Roethlisberger has actually been a hair more accurate, 28.2 percent of his throws have been off target this year compared to 28.3 percent in the past three years.
You would think that as Roethlisberger ages, he would start to lose his trademark ability to move outside the pocket on broken plays and find something down the field. But in a limited sample so far this year, he has still been effective when chased from the pocket — he has posted a 101.2 passer rating on just nine dropbacks in these situations this year compared with 124.2 on 93 dropbacks in the prior three seasons.
One logical explanation for Roethlisberger's poor start would be that something was amiss with his offensive line. Perhaps he's under more pressure than usual? But in fact, the Steelers QB is tied with Oakland's Derek Carr for the least pressured quarterback in the league this year — both have been under threat on just 15.1 percent of dropbacks. And that's the way it has been for a while in Pittsburgh; Roethlisberger had the second-lowest pressure rate in the league (behind Peyton Manning) from 2014-16.
So if Roethlisberger hasn't suddenly become inaccurate and he's not suddenly facing more pressure, the Steelers' offensive problems may extend beyond the QB and O-line.
Bell and Brown are not helping matters
The real explanation for Roethlisberger's poor start may be the decline in efficiency of his two top targets, wideout Antonio Brown and running back Le'Veon Bell.
On Roethlisberger's 62 targets to Brown this year, his passer rating has dropped to just 71, down from 112.2 on 480 targets in the past three years. And while it's hard to tell from a passer rating whether the quarterback or receiver is more to blame, other stats provide some evidence that the 29-year-old Brown is not quite himself this year. According to the NFL, defenses are playing Brown much more tightly at the snap — his average cushion has declined from 5.2 to 4.5 yards, one of the lowest among all receivers. But he's not making defensive backs pay by running by them, as his average separation is unchanged (2.9 yards).
Bell's receiving ability, meanwhile, is downright ordinary this year. The prior three years, Roethlisberger had 105 passer rating when throwing to Bell. This year, it's 85.4. Bell is averaging 3.85 yards before contact and just 1.48 after. The prior three years, those figures were 6.64 and 2.20. It's hard to blame Roethlisberger for Bell being unable to get open and make defenders miss.
Bell's ineffective performance so far has also meant that Roethlisberger can't use him as a safety valve, which has crushed the QB's stats against the blitz. In the past three seasons, Roethlisberger had a 96 rating on 381 dropbacks against blitzing defenses — mostly because the underneath pass to Bell was so effective. This year, his rating on those plays is down to 54.6, the lowest in the league.
Sunday, Roethlisberger travels to Kansas City to face the unbeaten Chiefs, who have been winning more with offense than defense, which may mean his receivers will be able to find a little more space. And Roethlisberger's attitude about his ability to perform has undergone a 180-degree turn. "They can question me. I don't question myself," he said, three days after his "Maybe I don't have it anymore" interview. "I think you guys are much more panicked than we are."
And unless Roethlisberger is a huge outlier and suddenly craters at age 35, or Bell and Brown have completely lost their ability to be dominant receiving threats, it seems there actually is little reason for Steelers fans to panic.
We looked at quarterbacks going back to 1978 to make sure all of them had played in the merged NFL for a decent amount of time. To qualify for the list, each quarterback needed to have a minimum of 125 pass attempts through five games.
More than 10 yards.
Michael Salfino is a freelance writer in New Jersey. His work can be found on The Athletic and the Wall Street Journal. @MichaelSalfino
NFL (568 posts) Pittsburgh Steelers (27) Ben Roethlisberger (5)

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Software quality: theory and management, 3rd edition, Bearswood Press.
Home / Who am I?
Alan Gillies has been Professor of Information Management at UCLAN since 1994. although he left full time academia in 2010.
These days he enjoys a portfolio career with roles as an Honorary Professor of Information Management and Managing Director at AGLC (Alan Gillies Learning Consultancy) Ltd, as well as Development Director at Care Aware International Ltd and the Register of Cancer Survivorship Professionals.
acted as advisor to the Regulatory Delivery, part of the Department for Business, Energy & Industrial Strategy.
operated as Director of Informatics and Evaluation at Hope Street Centre CIC in Liverpool.
been Development Director at Perform Learn Develop Ltd.
Health Informatics at UCLAN is 20 years old this year!
The NHS at 70. How informed are we?
My scrapbook is my personal collection of web resources I have found helpful, and you may too.


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20% discount applies to the following Intrepid Travel trips departing between 16 January 2020 and 03 March 2021.
· Uluru Adventure Original (PAR3-O/PAR3Y-O)
· Red Centre Adventure (PAR4-B, PAR4-O, PAR4Y-O, PAR4Y-B)
· Arnhem Land & Top End Adventure (PNTK5)
· Broome to Perth Overland (PBP10)
· Darwin to Broome Overland (PDB10)
· Adelaide to Alice Overland (PAASE7, PAASO7)
· Perth to Adelaide (PA9)
· Great Ocean Road Adventure Basix (PAMA-B and PAAM-B)
· Taste of Tasmania Basix (PNTW6-B)
10% discount applies to all other Intrepid Travel Australia trips departing between 16 January 2020 and 03 March 2021, excluding Arnhem Land and Uluru Camping Adventure (POBAU), Uluru and Arnhem Land Camping Adventure (POBUA), Northern Territory Encompassed Southbound (PKOSC), Total Territory Top End and Outback (POBTTC), Northern Territory Encompassed Northbound (POONC), Northern Territory Encompassed Northbound (ex Yulara) (POONCY), Melbourne to Darwin Overland (POMAD), Adelaide to Darwin Overland (POAAD), Uluru and Arnhem Land Camping Adventure (ex Yulara) (POBUAY), Brisbane to Cairns Northbound (PVOB), Sydney to Brisbane Northbound (PVON), Sydney to Cairns Northbound (PVOSC), Daintree Adventure (PVOD), East Coast Encompassed (PVSCD).
Discount applies to new bookings only made and deposited at between 16 January 2020 and 03 March 2020. Offer is valid for bookings made in AUD and NZD only for residents and travellers currently in Australia and New Zealand. The discount applies to the land tour price only and cannot be used in conjunction with any other offer and are not combinable. Discount does not apply to Tailor-Made Experiences, local payments/kitties, permits, additional travel arrangements, international and local airfares. Deposit of $99 per person per trip is required upon booking. If booking within 56 days of departure, full payment is due immediately. All tours are subject to availability. Prices are per person based on twin share accommodation, low season. Prices, itineraries and inclusions are subject to change without notice. Standard booking conditions apply.
Get up close to some of Mother Nature's finest creations while exploring WA's spectacular coast.
One of the world's most remote wine regions, Margaret River's wineries also produce some of the world's best drops. Sample chardonnay and cabernet sauvignon on a tasting tour of the region.
Embark on a hike like no other in Porongurup National Park. Cross towering eucalyptus forests and the famous Balancing Rock on a hike to the unique granite outcrop, Castle Rock.
Learn about Noongar culture on an illuminating bushwalk with a Wadandi custodian. Learn to identify native bush foods and medicines; discover the art of fire-lighting and tool-making, and be treated to a live didgeridoo performance inside Ngilgi Cave.
This trip is swag camping only, and whilst we think this adds to the experience, it might be an interesting style of accommodation for you
There are quite basic facilities on this trip, and one night with no shower available. National Parks are generally quite minimal with facilities offered
We will travel through some quite remote regions of the South West, most of the time we won't have phone reception or internet access
This trip requires a moderate level of fitness as it involves a lot of walking, allowing you to really get among nature. Please bring sturdy, comfortable walking shoes and comfortable clothing. You will need two pairs of shoes, one that can get wet.
This itinerary is valid for departures from 01 April 2018 to 31 March 2020.
This itinerary is valid for departures from 01 Apr 2018 to 31 Mar 2020.
View the itinerary for departures between 01 April 2020 - 31 March 2021
View the 2020 itinerary
Day 1: Perth to Fitzgerald National Park
Arrive in Western Australia's state capital. Though Perth has the distinction of being one of the world's most remote cities, it also boasts beautiful beaches, sprawling parks, a thriving craft beer scene and some pretty spectacular nearby scenery; as this tour doesn't involve any time in Perth, it's worth arriving a few days early to get to know this cosmopolitan city. Leave Perth bright and early on Day 1, as you head east for Fitzgerald River National Park via the Darling Ranges, also known as the Perth Hills. It's a beautiful drive through a leafy region of forested hills, charming country villages, scenic swim spots and boutique wineries. It's also a long drive – ten hours total – so the journey will be broken up with several stops. First stop: a coffee break in the morning in the historic township of York, WA's first inland town. Next is a stop for lunch by the unusual granite formation, Wave Rock, which is arched like a 15-metre high breaking ocean wave. Tonight, you'll camp Aussie-style in a swag beneath the WA sky at Fitzgerald River National Park.
Driving Time: about ten hours
Walking Time: about one hour
Camping (with basic facilities) (1 night)
Hippo's Yawn and Wave Rock
Tonight's campsite at Fitzgerald River National Park has a toilet but no shower facilities.
Day 2: Cape Le Grand National Park
Welcome in the day with a brisk hike up East Mt Barren, one of the three peaks that make up the Barren Range, for incredible views across the rugged coastline and waters of The Bight, or don't – it's your call. Sleep in if you'd prefer. Afterwards, hit the road, taking the scenic coastal route to Cape Le Grand National Park. It's a three-hour journey with stops along the way to properly take in the extraordinary surrounds – we're talking nine national parks, chalky white beaches (the sand at Lucky Bay was ranked 'Australia's whitest' twice), hidden bays and sunbathing kangaroos. You'll also stop for a coffee and a stretch in the charming little town of Esperance. After setting up camp at Cape Le Grand, there'll be a free afternoon for swimming, coastal bushwalks, lazing on the sand or whatever else your heart desires.
Driving Time: about three hours
Walking Time: about three hours
Tonight's campsite at Cape Le Grand National Park has toilet and shower facilities.
Day 3: Stirling Ranges
Begin the day with a morning bush walk to the top of Frenchman's Peak. It's a bit of a trek, but your effort is rewarded with sweeping views over the park's southern coastline and Recherche Archipelago. Following the walk, make tracks for the Stirling Ranges, a mountainous national park of rugged peaks, stark cliff faces, sheltered gullies and colourful wildflowers. The region is also renowned for its spectacular cloud formations, which are known to blanket the Range. Stop for lunch near Esperance along the way. Tonight, you'll swag camp at a private campground in the Stirling Ranges.
Driving Time: about six hours
Walking Time: about four and a half hours
Tonight's private campground in the Stirling Ranges has toilet and shower facilities.
Day 4: South West Coast
Embrace an early start and head to the Porongurup National Park for a hike through its unique landscape. Cross spectacular marri and karri forests and the famous Balancing Rock on a hike to Castle Rock, a huge granite outcrop. It's a bit of a climb to the summit, but the breathtaking views of the region make it worth the effort. Afterwards, set out on a scenic drive along WA's answer to Victoria's Great Ocean Road – Great Ocean Drive. Make sure to have your camera handy as you're treated to incredible coastal scenes; think postcard-perfect turquoise seas, dramatic red-rock cliffs and pristine beaches replete with perfect sands and sun-bleached boulders. Stop along the way to take a closer look at some of the area's natural attractions such as the Gap and Natural Bridge, Elephant Rocks and the largest tingle tree in the state.
Driving Time: about four hours
Walking Time: about one and a half hour
Tonight's accommodation at Quinninup Caravan Park has toilet and shower facilities.
Day 5: Margaret River
Begin the day with a visit to the famous Diamond Tree, a gigantic karri tree that was once used as a fire lookout. If you're feeling brave and aren't afraid of heights, climb the 50 metres to the lookout. Then you're off to encounter local Margaret River flavours with a tasting tour that will take you to some of the region's boutique wineries and breweries, chocolate factory and cheesery. See for yourself why Margaret River's wineries have built a reputation on their cabernet sauvignon and chardonnay.
Driving Time: about five hours
The Diamond Tree
Tonight's camp ground has toilet and shower facilities.
Day 6: Margaret River - Perth
Enjoy one last morning waking to the warble of kookaburras and cockatoos; this is the last day of your tour of the south-west corner of South Australia, but a memorable last day it is. Head to Dunsborough where local Wadandi custodian, Josh 'Koomal' Whiteland will shed insight into the world's oldest living culture. On a bushwalk led by Josh, learn to identify native bush foods and medicines; discover the art of fire-lighting and tool-making, and be treated to a live didgeridoo performance inside Ngilgi Cave. Continue to the tourist town of Busselton, which owes its popularity to beautiful Geographe Bay. Enjoy lunch and a swim in the turquoise waters of one of its excellent beaches before continuing to Perth, where the trip ends on arrival. There are no planned activities in Perth and you are free to depart at any time, though its usual for the group to get together and reflect on their journey over a few drinks and a meal.
Ngilgi Cave Entrance
Koomal Dreaming Aboriginal Cultural Experience
No accommodation is provided for tonight. If you plan on spending the night in Perth, please make sure to book your own accommodation prior to departure.
Swag Camping (5 nights)
There are currently no scheduled departures on our Esperance & Southwest Adventure trip. If you are interested in other trips in the region visit one of the links below.
Perth to Broome Overland
10 Days From 1796
Soak up the laidback lifestyle on Australia's West Coast from Perth to Broome. From...
Check out Australia's rugged west coast on a 10-day overland adventure from Perth,...
4WD Broome to Darwin Overland
Travel on an epic 4WD tour from the glistening beaches of Broome, across the wild...
Broome to Perth Overland
Soak up the laidback West Coast of Australia's on a 10-day adventure from Broome to...
4WD Darwin to Broome Overland
Embark on an eye-opening journey across Australia's rugged Top End, from balmy Darwin...
1. This trip starts in Perth at approximately 7 am and finishes on Day 6 approximately 7 pm. Onward travel to be booked the following day.
2. This trip requires a sleeping bag, you will need to provide your own.
3. This trip is basix swag camping.
4. Please note there is no single supplement is available for this trip.
5. This trip is for FIT AND ACTIVE people and involves very basic camping and challenging hikes.
As an Australian-owned business, we acknowledge the Traditional Owners of Country throughout Australia and their continuing connection to land, waters and community. We pay our respects to them and their cultures, and to their Elders past, present and future.
Call us 24/7 on 1300 797 010 or send us your enquiry below
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Here at Babbco Office Services Limited, we know how important it is to our clients that their move not only be quick and efficient, but also secure. We offer several services to help you feel safe putting your business in our hands before, during and after your office move. You can be confident that Babbco staff members assigned to your company's move are well trained and consistent. For clients that require extra security, we also employ the services of the city police and private company guards.
To best serve you, Babbco Office Services has protocols and procedures in place for all processes in our company so we're ready for any external issues that could arise. Everyone in our company has a contribution to make and we provide specific training for everyone at our firm who will come in contact with our customers. Whether through their customer care abilities, problem-solving skills or product and technical knowledge, each member of Babbco adds their own excellence to our team, helping our company stand out from our competition.


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DA Northern Cape Premier Candidate accompanies youngest son to school
by Andrew Louw – DA Northern Cape Premier Candidate
Today, like many parents and guardians across the Northern Cape, I accompanied my youngest son to school at the start of the school year.
Image removed by sender. Image removed by sender.
Munier will be continuing his studies at the Northern Cape High School in Kimberley.
Through giving our children basic education of a high quality, we give them the opportunity to become economically active adults. We give them the opportunity to pursue further studies, to start and grow their own businesses or to follow career paths of their choosing.
The DA is therefore committed to an education programme which will ensure that all children in all schools receive access to basic education of a high quality. In doing so, we equip our youth with the skills to contribute to the project of building One South Africa for All.
We wish all learners, parents and guardians, educators, and support staff all the best with the school year.
You can download the pictures here and here.
Andrew Louw
DA Northern Cape Premier Candidate
Tharina Whittaker


When we are called out to flea infestations, they're usually owing to cat fleas. It's incredibly rare to find human fleas within the UK. It can be difficult to get rid of cat fleas, as a flea-specific insecticide is occasionally imperative It is best to get a pest control professional in to receive with a bad infestation in Barnet NW9.
All of our pest control experts have been highly trained, and they all believe in prevention after getting rid of an infestation. This means that they will stay and inspect the premises, identifying where the pests have been entering the building. They'll then give you recommendations on how to preserve the building pest-free in Barnet NW9. Our fully-trained pest control engineers are available to handle rat infestations on a Twenty-four hours seven days a week basis. This is because rat infestations should be handled swiftly before the rats have had a chance to solve your issues and breed in Barnet NW9. All of the products that we use to eradicate pests and will proceed to pest control operations are both child and animal safe. We'd never use products that is acceptable to think that it is a risk to your safety or the safety of your family. Unfortunately, a slew of products that can be bought over the counter are unsafe in Barnet NW9. Copious amounts of people believe that rats will leave their commercial properties when the colder months of the year have passed, but unfortunately, that is not the case. Any pest control expert will be able to tell you that rats will in a diligent manner stay, as long as they know there is a food source nearby in Barnet NW9.
A pest control company with a great reputation is far more likely to get the job done properly in Barnet NW9.
Before committing to a pest control patch up permanently request a breakdown of the work that has been undertaken in Barnet NW9. Our pest control engineers are used to working in both domestic and commercial environments and are fully trained to handle a great choice of pest difficulties in Barnet NW9. Bedbugs can be a bloodsucking nightmare. They are not officially classified as a public health pest, but anyone who has experienced them will know how horrible they can be. A pest control engineer will be able to do away with out them for you in Barnet NW9. Sensible pest control is important as any pests that are not affected by the treatment could result in a further infestation. This is especially common in creatures that breed rapidly, such as rodents in Barnet NW9. Don't let your business suffer on account of infestation, call our pest control team today in Barnet NW9.
All of our pest control operatives continues the ability to that they need to identify where the pests have accessed your property. This means that they can advise you on the top of the range steps to take to prevent a further infestation in Barnet NW9.
The repair was excellent from the moment we called, and our pest control headaches were sorted fantastically in Barnet NW9. The pest control agent was professional and polite and gave an excellent level of mend in Barnet NW9. Human fleas are incredibly rare in the United Kingdom and other developed countries, but fleas that use other animals as hosts frequently use us as hosts when their desired host isn't close. Most fleas that hatch are on the floor, after falling off of our pets. When we walk by, the heat from our bodies awakens the dormant flea, usually resulting in a blocked to the ankle. A pest control company should be consulted if you feel like there is a bad infestation within your flat in Barnet NW9. Our pest control engineers are in a diligent manner called out to respond with rat infestations during the winter and other colder months. But, the rats that seek shelter from the cold will occasionally stay throughout the year if there is an active food supply in Barnet NW9. If you notice that there is an infestation within your business, then it is in your trump contact a pest control professional immediately in Barnet NW9.
If you own shop that is suffering from a cockroach infestation, it would be desirable to seek the professional recommendations of a pest control company in a flash. Cockroaches feed on virtually anything, which means that they can pick up diseases and transfer them onto almost anything in Barnet NW9.
Anyone who has ever experienced a bedbug infestation within their own how will know just how annoying they can be. They to give multiple lumps and itching in humans and have the potential to to give allergic reactions. These apple-pip sized creatures should be dealt with swiftly by a pest control specialist in Barnet NW9. Plenty of different pest infestations have the potential to be hazardous to both humans and animals alike, which is why pest control engineers are fully trained to handle any situation in Barnet NW9. If you're looking for a skilled and highly motivated pest control team, ring us today in Barnet NW9. Whatever the infestation issues you are facing, our experienced pest control team will have faced it before in Barnet NW9!
If you spot black garden ants within your flat you don't have to concern too much. They are more of a pain than they are a risk to human health, but sometimes they do nest too close to your home causing a quandary A pest control expert will be able to get rid of them effectively for you in Barnet NW9.
If you own shop that deals with food and one of your employees notice signs of a pest infestation, it is in your interest contact a pest control company in two shakes of a lambs tail. If there is an examination and you have done nothing to do away with the infestation, your business may well be closed in Barnet NW9.
Unfortunately, dust mites are almost impossible for pest control experts to eradicate. Insecticides don't work but a slew of harassing have located achievement using UV vacuum cleaners in Barnet NW9. Noticing that there are pests within your family home can be daunting, and while DIY solutions could potentially work they are usually short-term. A pest control engineer will be able to completely eradicate the problem or concern while also making sure that the pests will not return in Barnet NW9. More and more businesses are noticing Ghost Ant infestations, owing to the warm temperatures within heated buildings. These ants are unlike standard Black Garden Ants, and you should to continually contact a pest control company to junk them. Never experiment to chuck away an infestation on your own in Barnet NW9. For any cockroach infestation, we'd continually advise that you seek the aid and efficiencies of an expert pest control company. Cockroaches can be impossible to ditch even by experts in Barnet NW9. As an expert pest control company, we believe that every pest infestation should be handled swiftly Leaving an infestation could potentially result in an infestation that's harder to cure in Barnet NW9.
As with any industry, an experienced and reliable pest control patch up will ensure an excellent result in Barnet NW9.
Our pest control experts are fully trained to destroy cockroach infestations from both domestic and commercial properties, and they use insecticides to do so. Cockroaches are notoriously impossible to remove so it would be desirable to never experiment to do so on your own in Barnet NW9. As pest control experts, we believe in causing as little disruption in commercial buildings as we can. This is why we come out to survey the property before deciding on the top of the range steps to take. We can also wear discrete uniforms so that the reputation of your business isn't affected in Barnet NW9. We believe in the best of books so we never cut corners when it comes to pest control solutions in Barnet NW9. If you find pest droppings within your house it would be desirable to consult a pest control agency immediately. If all of the droppings look the identical then you surely have a pest problem within your property. A pest control professional will be able to identify the predicament and eradicate the pests for you in Barnet NW9. Businesses from across a range of sectors are reliant on pest control services at one time or another in Barnet NW9.
When it comes to pest control solutions, the most expensive option is not constantly the finest in Barnet NW9.
As pest control engineers, we believe that the control of the rat population is imperative Rats can carry a variety of both diseases and parasites, each of which can be harmful to humans and animals in Barnet NW9. Our pest control experts will be able to will diagnose the species of pest that has invaded your property fast finding out the exact extent of the problem or concern A plan can then be drawn to discard away the pests in Barnet NW9. If you notice a moth infestation within your house you should contact a guaranteed pest control technician as soon as possible. They'll be able to use insecticide or fumigation ways to chuck out away the infestation in Barnet NW9. Our experienced team considers every element of a pest control complication so you don't have to alarm in Barnet NW9. There are plenty of pests that we see more than others within the United Kingdom, but we are happy to welcome with the majority of pests. Please remember that no pest control company can welcome with bats, down to laws that are in put in put in place to safeguard them in Barnet NW9.
Wasps are not officially considered to be a risk to human health, but anyone that has been stung by a wasp will tell you the opposite. pest control treatments should be avoided unless the wasp nest is close to a location where it reasons a threat. For example, if someone living near the nest is elderly, or has severe allergies in Barnet NW9.
If your business premises is experiencing problems with pest control, contact our experienced team today in Barnet NW9. A pest control situation at your home can be horrible, especially if you have a young family. It can make your residence feel unclean, and leave you with a high level of anxiety in Barnet NW9. We understand the ultimate come true when dealing with a great choice of testing pest control problems in Barnet NW9. Pest control professionals are fully trained to receive with any mess that occurs within or around your home fast and professionally. The quicker you accept with a pest problem the quicker it goes away in Barnet NW9. Customer fix is an needed technology to make our clients feel at ease in the stressful situations that pest control difficulties raise in Barnet NW9.
Regardless of the type of problem or concern a pest control hiccup should be dealt with as promptly as possible in Barnet NW9.


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13 Jun 2012 // Latest Airline Route News // Comments OFF
Delta adds nine new routes from its New York JFK base
On 7 June, Delta Air Lines launched a total of nine new routes from its base at New York JFK, NY (JFK), the subject of one of this week's anna.aero airline analyses. One of the routes is operated by Delta mainline, while three are operated by Chatauqua and a further five by Pinnacle Airlines on Delta's behalf. All routes are served daily with the exception of Dayton, OH (DAY) which gets three daily flights. Six of the nine routes are not served by any other carrier, while the other three are flown by jetBlue, with American also providing competition on the route to Austin, TX (AUS).
Competition (WF)
Austin, TX (AUS) 7 American Airlines (7), jetBlue (14)
Charleston, SC (CHS) 7
Dayton, OH (DAY) 21
Greensboro, NC (GSO) 7
Elmira, NY (ELM) 7
Jacksonville, FL (JAX) 7 jetBlue (20)
Kansas City, MO (MCI) 7
Milwaukee, WI (MKE) 7
New Orleans, LA (MSY) 7 jetBlue (20)
Source: Delta, Innovata
WF: Weekly Frequency
AUS CHS DAY Delta ELM GSO JAX JFK MCI MKE MSY


This blend uses ceremonial grade Japanese matcha green tea and yerba mate to create long lasting, slow-release energy. We have added ginseng, baobab and maca powder for a 100% natural performance boost. A great alternative to coffee or sugar-based energy drinks.
During the day and mid-performance, with or without food.
To take hot, pour a dash of cold water over powder and stir into a paste. Then pour over boiling water and stir occasionally. To take iced, pour dash of hot water over powder and stir/shake into a paste. Add ice cold water. Goes well with any milk or smoothie.
Ceremonial grade Japanese matcha green tea (36%), yerba mate (12%), baobab, cinnamon, maca (8%), natural flavouring, pea protein, liquorice, Siberian ginseng, orange peel (2%). Contains liquorice - those suffering from hypertension should avoid excessive consumption.
"Yerba mate is so good for energy levels because it contains caffeine without the jittery side effects of a coffee. There is also good research on the Mission Tea burning fat, as it can help the body rely on fat for fuel during exercise. I would strongly recommend these products to any athlete or busy office worker."
Awarded best sports nutrition product 2019.
Running a marathon in every country in the world.
Our energy and perform teas contain roughly 30mg of caffeine per serving (about a third of the caffeine found in a coffee). Our recovery teas are caffeine free.
DO I NEED TO BE EXERCISING TO DRINK THE TEAS?
No. Although all of our blends are designed to be taken around physical performance, they're also a super healthy drink to keep you going at work or on a rest day.
CAN I DRINK THE TEAS COLD?
You certainly can. Simple instructions for cold brews can be found on all of our product pages.
DO ANY OF YOUR TEAS CONTAIN SUGAR?
ARE ALL OF YOUR TEAS DAIRY AND GLUTEN FREE?
Yes - got you covered.
Yes - we've been careful to ensure that each protein matcha contains plant-based protein only. Each is different to suit the flavour. Plant power!
ARE ALL THE INGREDIENTS 100% NATURAL?
Correct. All of our teas contain natural product only - you can check out the full ingredient lists on our product pages.
IS TEA SAFE TO DRINK DURING PREGNANCY AND BREAST FEEDING?
We suggest consulting your GP if you have any concerns during pregnancy or whilst breast feeding.
HOW DOES YOUR SUBSCRIPTION SERVICE WORK? ARE THERE ANY NASTY SURPRISES?
It works simply and we hate nasty surprises, so no. After subscribing to one of our products, you will be emailed a link where you can edit the time between deliveries or cancel your subscription. There is no minimum amount of time to subscribe with us and you can cancel at any time - just email tom@athleticteaco.com.
Enter your email to receive an exclusive 10% discount code and future offers on free samples.


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Ocasio-Cortez Crushes Fellow Dems – She's The Captain Now
Carmine Sabia
New York Rep. Alexandria Ocasio-Cortez is becoming the head of the Democrat Party is both voice and now in cash.
The 29-year-old representative has been a firecracker and a major driver of Democrat issues on Twitter and on the news.
And now she has crushed them in terms of fundraising as near $1.5 million has come to her campaign, The Daily Caller reported.
Ocasio-Cortez raised $1.42 million this past quarter, according to a report Tuesday from The New York Post. The congresswoman was followed in fundraising numbers by House Intelligence Committee Chairman Adam Schiff and House Speaker Nancy Pelosi, who raised $1.26 million and $1.145 million respectively for their campaigns, according to the Post.
While no House Democrats out-raised Ocasio-Cortez, several House Republicans did. House Minority Whip Steve Scalise raised $3.45 million, House Intelligence Committee Ranking Member Devin Nunes raised $2.6 million and House Minority Leader Kevin McCarthy raised $1.6 million, according to the Post.
U.S. Rep. Alexandria Ocasio-Cortez (D-NY) speaks to the thousands of people who participated in the People Climate March on October 11, 2019 in Copenhagen, Denmark. (Photo by Ole Jensen/Getty Images)
The report states that the vast majority of Ocasio-Cortez's donations were under $200, indicating strong grassroots support. The 30-year-old firebrand is facing a primary challenge from New York City Council Member Fernando Cabrera, who announced his congressional campaign last month. Cabrera referred to himself as a "moderate Democrat" who believes Ocasio-Cortez has neglected the needs of her district during her ascent on the national stage.
"This is very rare, unique — I can't recall anyone raising this much money during the first year in office," George Arzt, a political consultant, said in an interview with The New York Post.
"AOC is a celebrity who gained attention from people across the country, and many on the left support her," he said.
She defeated every other Democrat in the House, including the biggest names in her Party.
Rep. Jerrold Nadler (D-Manhattan-Brooklyn), chairman of the Judiciary Committee, raised $192,284 for the quarter and $860,037 since January.
Bronx Rep. Eliot Engel, who is facing a primary, raised $317,530 for the third quarter.
Her rookie sidekick, Michigan Rep. Rashida Tlaib, raised $722,212.
"Public education, libraries, & infrastructure policies (which we've had before in America and elsewhere in the world!) are not 'free stuff.' They are PUBLIC GOODS. And they are worth investing in, protecting, & advancing for all society and future generations. Sincerely, NY-14," she said.
"Earlier this year, Congress rushed to approve BILLIONS more $ for ICE + CBP. I saw members voting YES w/o even a summary of the bill. Nobody cared then how we'd pay for it. Now ICE is setting up fake universities to trap students. Yet we were called radical for opposing it.
"This is honestly one of the big reasons why the argument about "pay-fors" in healthcare, housing, etc so often are made in bad faith. I see decisions made every day that cost the American public billions of dollars a year for bogus reasons and nobody asks how we pay for it.
"None of the politicians who brand themselves "fiscally responsible" ever raise concern about rushing to shower ICE & CBP w/ $billions with 0 guardrails or oversight. None of them ask about how we pay for corrupt contracts or mass incarceration. Ask yourself why that is.
"Look out for those in politics who like to label themselves "fiscally responsible," yet only seem to care about the price of justice – not the cost of oppression. Everything has a price. And an unjust society is far costlier than one that invests in & values all people," she said.
JUST IN: Congress VOTES – It Passed 228 To 193
Ukraine President Gives The Order – Investigation Is On
She's OUT: Top Admin Official Leaves – White House In Shock
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«Happy Days» es el cuarto sencillo de la cantautora japonesa Ai Otsuka. Fue lanzado al mercado el día 7 de julio del año 2004 bajo el sello avex trax.

Información
El primer sencillo lanzado tras el primer álbum de estudio de Ai. Con este sencillo invitan por primera vez a Ai a participar en un comercial para la televisión, que en este primer caso fue para Ice Box de Morinaga, y también fue utilizado como tema imagen de un campeonato nacional en Japón donde participan varias universidades y estudiantes en concursos de sabiduría. En este sencillo hay un evidente cambio en su estilo musical, llevado por primera vez su música a ritmos mucho más típicos del Rock -con el claro elemento de la guitarra eléctrica-, pero de manera bastante liviana y sin alejarse del J-Pop y su imagen. En la canción utiliza la poco usual técnica de interpretar gran parte del tema por medio de un megáfono, y en el coro su voz se escucha con un tono mucho más agudo que el que regularmente usa, pero que es algo característico de ella y que se pudo apreciar por primera vez en "Sakuranbo".

Canciones

CD
 «Happy Days»

 «Happy Days» (Instrumental)
  (Instrumental)

DVD
 «Happy Days»

Sencillos de 2004
Sencillos de Ai Otsuka
Canciones sobre días

redpajama_set_name: RedPajamaWikipedia


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  ~ SPDX-License-Identifier: Apache-2.0
  ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~-->

<project xmlns="http://maven.apache.org/POM/4.0.0" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://maven.apache.org/POM/4.0.0 http://maven.apache.org/xsd/maven-4.0.0.xsd">
    <parent>
        <artifactId>spark_2.11</artifactId>
        <groupId>org.deeplearning4j</groupId>
        <version>1.0.0-SNAPSHOT</version>
    </parent>
    <modelVersion>4.0.0</modelVersion>

    <artifactId>dl4j-spark-nlp-java8_2.11</artifactId>
    <packaging>jar</packaging>

    <name>dl4j-spark-nlp-java8</name>

    <properties>
        <project.build.sourceEncoding>UTF-8</project.build.sourceEncoding>
        <hazelcast.version>3.4.2</hazelcast.version>
    </properties>

    <dependencies>
        <dependency>
            <groupId>org.deeplearning4j</groupId>
            <artifactId>deeplearning4j-nlp</artifactId>
            <version>${deeplearning4j.version}</version>
        </dependency>
        <dependency>
            <groupId>org.deeplearning4j</groupId>
            <artifactId>dl4j-spark_2.11</artifactId>
            <version>${project.version}</version>
        </dependency>
        <dependency>
            <groupId>org.nd4j</groupId>
            <artifactId>nd4j-parameter-server-node_2.11</artifactId>
            <version>${nd4j.version}</version>
            <exclusions>
                <exclusion>
                    <groupId>net.jpountz.lz4</groupId>
                    <artifactId>lz4</artifactId>
                </exclusion>
            </exclusions>
        </dependency>
        <dependency>
            <groupId>junit</groupId>
            <artifactId>junit</artifactId>
            <scope>test</scope>
        </dependency>

        <dependency>
            <groupId>org.apache.spark</groupId>
            <artifactId>spark-core_2.11</artifactId>
            <version>${spark.version}</version>
            <scope>provided</scope>
        </dependency>

        <dependency>
            <groupId>org.deeplearning4j</groupId>
            <artifactId>deeplearning4j-common-tests</artifactId>
            <version>${project.version}</version>
            <scope>test</scope>
        </dependency>
    </dependencies>

    <profiles>
        <profile>
            <id>test-nd4j-native</id>
        </profile>
        <profile>
            <id>test-nd4j-cuda-10.2</id>
        </profile>
    </profiles>

</project>

redpajama_set_name: RedPajamaGithub


and a professionaly musician – cello player.
Specialised for sustainable development of cities.
Expert for sustainable development at UR Institute.
Specialised for software engineering, mobile & embedded computing and Internet of Things (IoT).
Junior researcher at Instituto de Telecomunicações, Portugal.
Specialised in Fine art & Postmodern art (BioArt, AV performances, experimental sound art, installation and interactive art).


A mysterious figure has broken into Mayuri Kurotsuchi's laboratory in the Seireitei. Using a scythe-like weapon, the intruder causes Mayuri to go mad and destroy his own lab equipment. Kenpachi rushes to the laboratory as the Seireitei becomes engulfed in a cloud of reishi. When Kenpachi arrives he is greeted by an even greater explosion of reishi that completely devastates the Seiretei. Rukia witnesses this catastrophe from a distance, when the two intruders approach her and use the same scythe that drove Mayuri mad. The intruders then abduct Rukia as she feels something inside of her fade away. Meanwhile, in the World of the Living, Ichigo and Kon experience a strange disturbance and head to Kisuke Urahara's shop for some answers.


text:
package archive

// Debian package

// STATUS: 1%

import (
	"os"

	"github.com/martinlindhe/formats/parse"
)

// DEB parses the deb format
func DEB(c *parse.Checker) (*parse.ParsedLayout, error) {

	if !isDEB(c.Header) {
		return nil, nil
	}
	return parseDEB(c.File, c.ParsedLayout)
}

func isDEB(b []byte) bool {

	s := string(b[0:21])
	return s == "!<arch>\n"+"debian-binary"
}

func parseDEB(file *os.File, pl parse.ParsedLayout) (*parse.ParsedLayout, error) {

	pos := int64(0)
	pl.FileKind = parse.Archive
	pl.MimeType = "application/vnd.debian.binary-package"
	pl.Layout = []parse.Layout{{
		Offset: pos,
		Length: 21, // XXX
		Info:   "header",
		Type:   parse.Group,
		Childs: []parse.Layout{
			{Offset: pos, Length: 21, Info: "magic", Type: parse.ASCII},
		}}}

	return &pl, nil
}